WASHINGTON (CNN) -- The 11th hour came and went, and Congress failed to meet a midnight ET deadline to pass a funding bill that would keep the federal government running.

It is the first federal government shutdown in 17 years.

Defying repeated rejections by the Democratic-led Senate, House Republicans on Monday again attempted to derail Obamacare by amending a spending plan that would avert a government shutdown. The measure would delay the individual mandate in the health care law and eliminate health premium subsidies for members of Congress, their staff and the president.

With a government shutdown looming, politicians in Washington talked mostly at each other Monday instead of negotiating a way to avoid it.

In the latest volley of legislative ping pong over a short-term spending plan needed to avoid a shutdown at midnight, Senate Democrats again rejected a House proposal that also would derail Obamacare.

The 54-46 Senate vote on strict party lines returned the focus to the Republican-led House, where Speaker John Boehner said another effort would be made to attach provisions that would delay President Barack Obama's signature health care reforms from full implementation starting Tuesday.

Despite repeated rejection by the Democratic-led Senate and a veto threat by Obama, House Republicans will raise the stakes on the spending plan by also voting on a provision to force the president and members of Congress to get private health coverage under Obamacare instead of the government health care program, Boehner said.

Obama made a previously unscheduled statement to reporters on Tuesday afternoon that repeated his criticism of the repeated attempts by House Republicans to undermine Obamacare that he said no threatens to harm the economy with a shutdown.

"You don't get to extract a ransom for doing your job, for doing what you're supposed to be doing anyway, where just because there's a law there that you don't like," Obama said.

The president later called Boehner and other party leaders in the House and Senate, the White House said, but a Boehner spokesman indicated there was no breakthrough.

Rebellion Against Speaker Boehner?Meanwhile, GOP sources told CNN that moderate House Republicans were trying to galvanize what would amount to a rebellion against Boehner and their tea party colleagues by defeating the latest proposed spending plan with attached anti-Obamacare provisions.

However, a procedural vote on the measure passed with only six Republicans voting "no," ensuring floor debate would proceed with a final vote set for later Monday night.

Without congressional approval of new spending legislation, parts of the federal government will begin shutting down when the current fiscal year ends at midnight, forcing agencies to furlough thousands of workers and curtail some services until there is a resolution.

"I feel sad about it. We expect more from our Congress," said Vick Temple, a worker for the Federal Aviation Administration who told CNN he faced being furloughed in a shutdown.

Polls show public opposition to a shutdown, and stocks ended lower Monday on Wall Street due to concerns over the economic impact.

However, House Republicans decided to try again to force the Senate Democrats to back down by planning to attach more anti-Obamacare provisions to a third version of the short-term spending plan needed to keep the government funded for several weeks beyond Monday.

In addition, Boehner and other House GOP leaders said they would add the so-called nuclear option that would force Democrats to essentially vote in favor of giving themselves and their staff members government subsidies for health coverage.

The Obamacare subsidies are similar to the health care coverage that private employers provide their workers. Under the House GOP provision, Obama and members of Congress as well as their staff would obtain health coverage through the private exchanges of Obamacare that go into effect on Tuesday.

GOP Rep. James Lankford of Oklahoma told CNN that the Affordable Care Act was written to ensure that politicians in Washington would receive the same health care options and costs as people who purchase private health coverage within the program.

"I think it's right to have employer provided health care, but the way the law is written, it's not allowed," Lankford said.

Meanwhile, the two parties persisted in blaming the other side as the shutdown deadline neared.

Republican Rep. Renee Ellmers of North Carolina said on CNN's "New Day" that her party continues to be deeply concerned about Tuesday's scheduled opening of Obamacare health insurance exchanges and "keeping the checkbook out of Barack Obama's hands and the damage can be done there."

Get up to speed on the showdown:Rep. Debbie Wasserman Shultz, D-Florida, appearing alongside Ellmers, characterized the Republican strategy of tying overall government operations to at least a delay in health care changes as "irrational."

"It jeopardizes the economy and it makes no sense," she said.

On Monday morning, Obama told reporters he wasn't resigned to a shutdown, but he signaled its likelihood even as he indicated possible talks with congressional leaders.

"I suspect that I will be speaking to the leaders today, tomorrow and the next day," Obama said at a joint appearance with visiting Israeli Prime Minister Benjamin Netanyahu, who acknowledged the Washington brouhaha by thanking the president for meeting with him "on what I know is a very busy day for you."

The latest plan rejected by Senate Democrats would have delayed Obamacare for a year and repealed a tax on medical devices.

Legislative ping pong:Last week, the Senate voted down a House GOP plan to eliminate funding for Obamacare in a short-term spending plan to keep the government running in the new fiscal year that begins Tuesday.

Democrats have pressured Boehner to give up a losing fight over Obamacare forced by tea party conservatives and instead hold a vote on a "clean" spending plan that includes no provisions seeking to undermine the health care reforms.

On CNN, Wasserman Schultz predicted that such a measure would pass easily with support from all Democrats and more moderate Republicans.

Some Republicans expressed frustration Monday with the tactics of their congressional colleagues. Veteran GOP Sen. John McCain of Arizona noted that any attempt to repeal Obamacare would fail because of Obama's veto, which would require a two-thirds majority in the Senate to overcome.

"There's not 67 votes in the United States Senate, therefore, ergo, we're not going to repeal Obamacare," McCain said. "Okay? That's it. We may do this for a day. We may do it for a week. We may do it for a month. It's going to end up the same way. "

GOP Rep. Charlie Dent of Pennsylvania told CNN Chief Congressional Correspondent Dana Bash that whichever party was to blame, a shutdown will make everyone look bad.

"At this point, the hourglass is nearly empty," Dent said. "Now that we've sent over two volleys to the U.S. Senate and they rejected both."

Trying again would only yield the same result, he continued, adding that "sooner or later, we have to pass a clean resolution to fund the government before the end of the day."

"I believe the votes are there to do it," Dent said.

Obamacare is the GOP focus:Obama and Democrats reject what they call Republican efforts to use the threat of a government shutdown to force negotiations on the president's signature health care reforms.

Noting that the 2010 Affordable Care Act has been upheld by the Supreme Court, they say it is settled law that voters endorsed last year by re-electing Obama over GOP candidate Mitt Romney, who campaigned on repealing it.

A new CNN/ORC poll shows that Americans are not happy about the prospect of a shutdown, which is happening because Congress has been unable to pass a budget for the new fiscal year that begins Tuesday.

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